The Coherent Point Drift Algorithm Adapted for Fixtureless Metrology of Non-rigid Parts

Abstract

Unlike the metrology of rigid parts, no viable and industrial solutions in the case of non-rigid parts are available. Due to gravity load and residual stress, non-rigid parts (flexible, compliant) may have in a Free State condition a significant different shape than their corresponding nominal geometry (CAD model). As a result, very expensive and specialized fixtures mounting are needed by the industry to constrain the component during the inspection. Dealing with this real industrial problem, this paper proposes a new method to inspect non-rigid parts without these specialized fixtures. In this method, the CAD model is smoothly modified to fit the scanned part respecting two criteria that belong to non-rigid parts. The first criterion is the isometric transformation (or the condition that stretch should be very small) between the original CAD model and the modified one. The second criterion is the Euclidian distance between the modified CAD model and its corresponding scanned part. The proposed approach consists of adapting the Coherent Point Drift powerful non rigid registration method to meet the specifications of non-rigid parts. In other words, by minimizing the two above criteria, the paper proposes a ‘flexible’ registration to align the scanned manufactured compliant part to its nominal model in order to compare them and to deliver an inspection report. Satisfying results were obtained when validating the proposed method on a case study taken from the aerospace industry. The low percentage of error between the estimated value of defect and the reference one reflect the effectiveness of the proposed approach.